Abstract. In this paper, we study right half-plane harmonic mappingsf 0 and f, where f 0 is xed and f is such that its dilatation of a conformalautomorphism of the unit disk. We obtain a sucient condition for theconvolution of such mappings to be convex in the direction of the realaxis. The result of the paper is a generalization of the result of by Li andPonnusamy [11], which itself originates from a problem posed by Dor etal. in [7]. 1. IntroductionLet D = fz2C : jzj<1gbe the unit disk. We will consider the family ofcomplex-valued harmonic mapping f= u+ ivde ned in a domain DˆC ifuand vare real harmonic in D, i.e., u= v= 0, where is the complexLaplacian operator = 4@ 2 @z@z:=@ 2 @x 2 +@@y 2 :Denote by Hthe class of all complex-valued harmonic mappings f in D nor-malized by f(0) = f z (0) 1 = 0. Let S H be the subclass of Hconsisting ofunivalent and sense-preserving functions. For a simply connected domain D,such functions can be written in the form f= h+ g, where(1) h(z) = z+X